This document was last updated at 2019-07-25 23:06:37.

This document is dedicated to the confirmatory choice analyses that were proposed for Experiment 2.

Design

The design is 2 (difficulty: easier than reference vs. harder than reference) X 2 (difference: moderate vs. extreme). The analysis is a 2 X 2 within-subjects ANOVA on the proportion selection of the safe deck.

Predictions

The critical prediction hinges on the main effect of difficulty. The prospect model predicts that choices will be risk averse when all outcomes are easier (or equal to) the reference deck, and that choices will be risk seeking when all outcomes are harder (or equal to) the reference deck. The predictions are visualized below:

All other hypotheses predict that choices won’t depend on difficulty. Concave up and down predict that choices, overall, will either be risk averse or risk seeking, respectively.

Results

The cleaned data can be seen below

dst <- read.csv('../../../data/dstClean.csv')
n <- dst %>% 
  group_by(subject) %>% 
  summarize(n()) %>% 
  nrow()
dst

The sample size is 53.

Visualize the Results

I’ll first visualize the results broken down across the whole design, followed by a breakdown by only the critical difficulty variable.

dst <- dst %>% 
  mutate(difference = factor(difference, levels = levels(difference)[c(2,1)]),
         selSafeDeck = ifelse(selectedRiskyDeck == 1, 0, 1))
dst %>% 
  group_by(subject, difference, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difference, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd, group = difference)) +
  geom_bar(stat = 'identity', aes(fill = difference), color = 'black', position = position_dodge(width = 0.9)) + 
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), position = position_dodge(width = 0.9), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) +
  ylim(0, 1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  scale_fill_manual(name = 'Difference', values = c(Moderate = 'light grey', Extreme = 'black')) +
  theme_bw()

Main effect of difficulty:

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(selSafeDeck = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(selSafeDeck), se = sd(selSafeDeck) / sqrt(n)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) + 
  geom_bar(stat = 'identity') +
  geom_errorbar(aes(ymin = ssd - se, ymax = ssd + se), width = 0.5) +
  labs(
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Dashed line represents selecting at chance'
  ) + 
  ylim(0,1) +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  theme_bw()

Visualize subject data underlying the difficulty variable:

condMeans <- dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  group_by(difficulty) %>% 
  summarize(ssd = mean(ssd))

dst %>% 
  group_by(subject, difficulty) %>% 
  summarize(ssd = mean(selSafeDeck)) %>% 
  ggplot(aes(x = difficulty, y = ssd)) +
  geom_violin(fill = NA, alpha = 0.2) + 
  geom_boxplot(fill = NA, alpha = 0.2) +
  geom_point(alpha = 0.4) +
  geom_line(aes(group = subject), alpha = 0.4, linetype = 'dotted') +
  geom_point(data = condMeans, aes(x = difficulty, y = ssd), size = 4, shape = 23, color = 'black', fill = 'red') +
  geom_hline(yintercept = 0.5, linetype = 'dashed') +
  geom_label(data = condMeans, aes(x = difficulty, y = ssd, label = round(ssd, 2)), hjust = 1.5, vjust = 1.5) +
  ylim(0,1) + 
  theme_bw() +
  labs(
    title = 'Selection of safe deck by difficulty and subject',
    x = 'Difficulty',
    y = 'Proportion Selection of Safe Deck',
    caption = 'Red diamond reflects condition means. Horizontal, black, solid lines reflect medians.'
  )

Statistics

m1 <- ezANOVA(wid = subject, within = .(difference, difficulty), dv = selSafeDeck, data = dst, detailed = TRUE)
## Warning: Converting "subject" to factor for ANOVA.
## Warning: Collapsing data to cell means. *IF* the requested effects are a
## subset of the full design, you must use the "within_full" argument, else
## results may be inaccurate.
data.frame(m1$ANOVA)
 

A work by Dave Braun

dab414@lehigh.edu